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Top1. Introduction
Recently, numerous works and studies have noted and discussed the emerging and trends in the IoT’s development and its role in the modern infrastructure of the human environment (Al-Ansi et al., 2021; El-Latif et al., 2020; EL-Latif et al., 2019; Ge et al., 2014; Muthanna et al., 2017; Network 2030, n.d.). In addition, IoT networks already have a significant density of devices (the number of devices per unit area), and it’s expected to reach to one device per square meter, in the near future. Moreover, we note that, the high-density in the local networks have been existing for a long time, such as wireless access (Wi-Fi) in stadiums and similar facilities, where the network structure is regular and contains a sufficiently large number of access points, that are evenly distributed in the service area, taking into account the characteristics of the structure (Kaur et al., 2019; Yang, 2020). However, IoT networks will be built in a wide variety of elements of the infrastructure of settlements, as well as on natural objects, for example, such as river banks, mountains and forests, sea coasts, etc. In such conditions, the external environment determines the possible structure of the placement of network nodes. In this case, the shape of the network repeats the shape of those objects in which it is built (Abbas, 2021; Abd EL-Latif et al., 2020; Abou-Nassar et al., 2020; Elgendy et al., 2020; Zhang et al., 2020).
Most of the current studies were focused on using an obvious approach which copies the environment properties of the target network, i.e., drawing up a plan and transferring it in some way to the environment of the network model. This approach is implemented by many systems, in which wireless communication networks are simulated and therefore, has the advantage of the maximum similarity of the model structure with the structure of the target network (Al Shidhani, 2019; Sotnik, 2020). Whereas, the main drawbacks of this approach are inherent in all numerical methods and lies in the fact that it gives a particular solution and does not allow generalization and analysis of the relationship between the parameters of the environment and the target network (Devo et al., 2020).
This analysis requires a lot of simulation experiments, analysis and generalization of their results. Solutions give an effect with a significant individuality of conditions, instability of structures, which takes place with a relatively small number of network elements. In high-density networks, the number of network elements is so great that the formed network structures can be quite “stable”, this allows generalizations to be made and establish connection with the structure of the environment (Zhang, 2020).
Furthermore, most of the objects in the environment in which the network is created, i.e., natural and architectural objects have the properties of fractal figures (FF) (Image Processing and Analysis in Java, 2021; Paramonov et al., 2020). Moreover, a common denominator of most of these developments (Chen et al., 2017; Falconer, 1952) is that the self-similar structure of such objects is proved. Additionally, the numerical characteristic of the shape in this case is the fractal dimension (FD) and the concept of which was just introduced in the study of self-similar objects (Falconer, 1952; Paramonov et al., 2020; Soumya, 2017).